Almost perfect sequences based on cyclic difference sets

The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.

The structural analysis of protein sequences based on the quasi-amino acids code

Proteomics is the study of proteins and their interactions in a cell. With the successful completion of the Human Cenome Project, it comes the postgenome era when the proteomics technology is emerging. This paper studies protein molecule from the algebraic point of view. The algebraic system （∑, ＋, ＊） is introduced, where ∑ is the set of 64 codons. According to the characteristics of （∑, ＋, ＊）, a novel quasi-amino acids code classification method is introduced and the corresponding algebraic operation table over the set ZU of the 16 kinds of quasi-amino acids is established. The internal relation is revealed about quasi-amino acids. The results show that there exist some very close correlations between the properties of the quasi-amino acids and the codon. All these correlation relationships may play an important part in establishing the logic relationship between codons and the quasi-amino acids during the course of life origination. According to Ma F et al （2003 J. Anhui Agricultural University 30 439）, the corresponding relation and the excellent properties about amino acids code are very difficult to observe. The present paper shows that （ZU, ＋,×） is a field. Furthermore, the operational results display that the eodon tga has different property from other stop codons. In fact, in the mitochondrion from human and ox genomic codon, tga is just tryptophane, is not the stop codon like in other genetic code, it is the case of the Chen W C et al （2002 Acta Biophysiea Siniea 18（1） 87）. The present theory avoids some inexplicable events of the 20 kinds of amino acids code, in other words it solves the problem of ＇the 64 codon assignments of mRNA to amino acids is probably completely wrong＇ proposed by Yang （2006 Progress in Modern Biomedicine 6 3）.

Almost sure limit theorem for the maximum of a class of quasi-stationary sequences

This paper investigates the problem of almost sure limit theorem for the maximum of quasi-stationary sequence based on the result of Turkman and Walker. We prove an almost sure limit theorem for the maximum of a class of quasi-stationary sequence under weak dependence conditions of D （uk, un） and αtm,ln = 0 （（log log n）-（1＋ε））.

PERFECT PUNCTURED BINARY SEQUENCE PAIRS

This paper presents the definition of perfect punctured binary sequence pair and the combinatorial admissible conditions for searching the perfect punctured binary sequence pairs and proves that all of the pseudo-random binary sequences satisfy these conditions. Computer calculation verifies that the pseudo-random binary sequences with length up to N=127 can be easily turned into perfect punctured binary sequence pairs.

Constructions for almost perfect binary sequence pairs with even length

The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs(DDSPs) are also derived.

Accuracy Analysis for 6-DOF PKM with Sobol Sequence Based Quasi Monte Carlo Method

To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions,can prevail traditional Monte Carlo method with up to 98. 59% and 98. 25% enhancement for computational precision of pose error statistics.Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

A NEW SYNCHRONIZATION SCHEME USING PERFECT PUNCTURED BINARY SEQUENCE PAIRS IN DS-UWB SYSTEM

Ultra WideBand (UWB) radio is a new wireless technology that transmits extremely short duration radio impulses. In this paper, a new synchronization scheme is proposed in Direct Sequence (DS) UWB system using Perfect Punctured Binary Sequence Pairs (PPBSP) as the preamble. It can acquire both Pseudo-Noise (PN) sequence and frame synchronization at the same time. The properties and the combinatorial admis sibility conditions of PPBSP are presented. The simulation results show that PPBSP is good for synchronization by their good cross-correlation properties both under Additive White Gaussian Noise (AWGN) channel and modified Saleh-Valenzuela channel.

Solidification sequence and as-cast microstructure of a model Pb-Bi-Sn alloy with quasi-peritectic reaction

The Pb39 Bi25 Sn36 alloy was directionally solidified at varied withdrawal rates followed by quenching.From metallographic observation,composition analysis and differential scanning calorimetry(DSC)analysis,the solidification sequence of Pb39 Bi25 Sn36 alloy was characterized.The Sn-dendrite is observed as the primary phase during solidification,followed by theβ(Pb7 Bi3)/Sn divorced eutectic.At lower temperatures,theβ(Pb7 Bi3)/Sn binary eutectic is formed in the interdendritic region.However,the quasi-peritectic reaction[L+α-Pb→β(Pb7 Bi3)+Sn]does not occur as the prediction based on ternary phase diagram analysis,which can be attributed to the unequilibrium solidfication condition.Moreover,the as-cast microstructure is significantly refined with the increasing withdrawal rates.The quenched sample only exhibits the lamellar structure of Sn,β(Pb7 Bi3)and Bi phases.The results can provide instructions to optimize the as-cast microstructure of ternary alloys with quasi-peritectic reaction.

DNA Sequencing by Capillary Electrophoresis Using Quasi-inter-penetrating Network Formed by Polyacrylamide and Poly(N-hydroxymethylacrylamide)

Quasi-interpenetrating network formed by polyacrylamide and poly （N-hydroxymethylacrylamide） was designed, synthesized, and tested for DNA sequencing by capillary electrophoresis. The performance of quasi-IPN on DNA sequencing was determined by the acrylamide to N-hydroxymethylacrylamide molar ratio and sequencing temperature.

Convergence of Iterative Sequence with Mixed Errors for Uniformly Quasi-Lipschitzian Mappings

In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results.

低相关区互补序列集的构造方法研究

完备互补序列是一类具有理想相关函数性质的信号,在多址接入通信系统、雷达波形设计等领域具有广泛的应用。然而完备互补序列集合大小不超过其子序列数目。为扩展互补序列数目,该文研究了非周期低相关区互补序列集的构造方法,首先提出了两类有限域上的映射函数,进而得到两类参数渐近达到最优的低相关区互补序列集。该类低相关区互补序列集相比完备互补序列集具有更多的序列数目,在通信系统中可支持更多的用户。

不相关多子集零相关区序列集的构造

在多小区环境下的准同步码分多址(quasi-synchronous code-division multiple-access,QS-CDMA)系统中,不相关多子集零相关区(zero correlation zone,ZCZ)序列集不仅可以消除一定时延内来自相同小区的信号干扰,而且可以完全消除来自相邻小区的信号干扰。针对如何基于仿酉矩阵构造多子集ZCZ序列集的问题,设计了两种构造方法。具体地,通过构造具有一定特性的多个初始矩阵,再结合仿酉矩阵,进而利用不同的初始矩阵产生不同的ZCZ序列集,且序列集间互不相关。所提方法的核心是多个初始矩阵的设计,方法1通过对离散傅里叶变换(discrete Fourier transform,DFT)矩阵进行分块与叠加实现,方法2利用已有的不相关多子集ZCZ序列集实现。由两种方法得到的构造结果,其参数趋近于最优,为解决多小区环境下的干扰抑制问题提供了新的序列设计方法。

基于双序列反序的(4,L)规则girth-8 QC-LDPC短码

围长较大的短码长准循环(QC)低密度奇偶校验(LDPC)码的显式构造对于QC-LDPC短码的理论研究与工程应用具有重要意义。首先提出一种基于成对策略的贪婪搜索算法,并根据此算法在列重J为4时的经验结果,归纳总结出一种具有双序列反序特征的指数矩阵。随后证明了该指数矩阵对于任意行重L均对应于围长为8的QC-LDPC码。与现有的典型显式构造方法即最大公约数(GCD)方法相比,新QC-LDPC码提供的码长显著降低。最后,将指数矩阵的拆分拼接和掩膜处理技巧与新QC-LDPC码结合起来,设计出了译码性能在高信噪比区超过5G NR LDPC码的合成码。

基于有限Zak变换的零相关区序列集构造

针对Brodzik在2011年和2013年文中的完备序列和零相关区序列构造中参数的限制问题,分别提出完备序列和零相关区序列的新构造方法。首先,基于有限Zak变换,提出没有“参数为奇素数”限制的完备序列构造结构,并且用同余理论论证。其次,提出一种具有稀疏性、结构化特点的L×KL的零相关区序列集的Zak空间结构,从而得到零相关区序列集,用有限Zak变换和同余理论论证。相比Brodzik 2013年文中的零相关区序列集,新构造的零相关区序列集的零相关区的长度更长,序列的数量更多。

Quasi-principally k-projective Semimodules

In this paper,we principally introduce the concept of quasiprincipally k-projective semimodules,on the basis of the theories of k-projective semimodules and quasi-principally modules,we get some good properties of quasi-principally k-projective semimodules,therefore generalize some properties of quasi-principally modules of ring and k-projective semimodules of semiring to quasi-principally k-projective semimodules of semiring.

Perfect Matrix Algebras ∑(λ)(Ⅱ)-AK-Property

In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, KSthe （LF）-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.

基于Stanley序列的QC-LDPC码新颖构造方法

针对准循环低密度奇偶校验(quasi-cyclic low-density parity-check,QC-LDPC)码的短环结构会严重影响码字纠错性能的问题,基于Stanley序列(Stanley sequence,SS)提出一种围长至少为8的QC-LDPC码新颖构造方法。从Stanley序列中选取某些特定元素构成一个呈递增关系的集合,利用穷举算法搜索出满足无环4和环6条件的元素得到另一个递增集合,构造相应的指数矩阵,得到其奇偶校验矩阵。仿真结果表明,在误码率(bit error rate,BER)为10-6时,所构造的SS-QC-LDPC码与同码率码长的其他QC-LDPC码码型相比,其净编码增益均有一定提升,因而其纠错性能较好,且无错误平层现象。此外,该构造方法的计算复杂度较低。